A History of Mathematics |
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Page 22
... quantities by him and his school will be taken up under the head of arithmetic . According to Eudemus , the Pythagoreans invented the prob- lems concerning the application of areas , including the cases of defect and excess , as in ...
... quantities by him and his school will be taken up under the head of arithmetic . According to Eudemus , the Pythagoreans invented the prob- lems concerning the application of areas , including the cases of defect and excess , as in ...
Page 68
... quantities a , b , c , d were said to be in arithmetical proportion when abc - d ; in geometrical proportion , when a : bc : d ; in harmonic proportion , when a bb - ca : c . It is probable that the Pythagoreans were also familiar with ...
... quantities a , b , c , d were said to be in arithmetical proportion when abc - d ; in geometrical proportion , when a : bc : d ; in harmonic proportion , when a bb - ca : c . It is probable that the Pythagoreans were also familiar with ...
Page 69
... quantities , which is attributed by Eudemus to the Pythagoreans . It was indeed a thought of extraordinary boldness , to assume that straight lines could exist , differing from one another not only in length , that is , in quantity ...
... quantities , which is attributed by Eudemus to the Pythagoreans . It was indeed a thought of extraordinary boldness , to assume that straight lines could exist , differing from one another not only in length , that is , in quantity ...
Page 70
... quantities at length . He investi- gates every possible variety of lines which can be represented by √ √ √b , a and b representing two commensurable lines , and obtains 25 species . Every individual of every species is ...
... quantities at length . He investi- gates every possible variety of lines which can be represented by √ √ √b , a and b representing two commensurable lines , and obtains 25 species . Every individual of every species is ...
Page 73
... quantities in integral numbers are to be found . It may be stated thus : The sun had a herd of bulls and cows , of different colours . ( 1 ) Of Bulls , the white ( W ) were , in number , ( + ) of the blue ( B ) and yel- low ( Y ) : the ...
... quantities in integral numbers are to be found . It may be stated thus : The sun had a herd of bulls and cows , of different colours . ( 1 ) Of Bulls , the white ( W ) were , in number , ( + ) of the blue ( B ) and yel- low ( Y ) : the ...
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